Fig. REF  displays the evolution of a linear scalar perturbation field on the background of the BH solution (REF )-(). The most obvious effect we can observe is the emergence of echoes following the initial quasinormal ringdown. This pattern becomes more evident for higher \(\ell \)  due to the fact that more energy is carried away from the PS when perturbed. For spherically-symmetric \(\ell =0\)  perturbations, on the other hand, the echo pattern is not so evident since the field does not excite the PS significantly, therefore the echoes fall off rapidly. Our investigation confirms that the decay rate of scalar perturbations follows an exponential fall-off, as in [1]}, [2]}, which is more evident for the case of \(\ell =0\) . This behaviour is in contrast to that of asymptotically flat BH perturbations, where the quasinormal ringing gives way to a power-law cutoff [3]}, [4]}, [5]}, and its occurrence is related to the asymptotic nature of timelike infinity in AdS spacetimes which serves as a reflective boundary. The echoes have significantly smaller amplitudes compared with the initial ringdown, which is in agreement with the studies in [6]}, [7]}, [8]} and the dissipative nature of the event horizon, designating modal stability.
